Suleiman announced his bid for the presidency Friday in Cairo after hundreds of supporters conducted a rally during which they called for him to run, Ahram Online reported.
"The revolution rejected him as vice president, and he still wants to run for president," said a statement Friday from the Freedom and Justice Party.
Mubarak was ousted after three decades as president and is on trial for allegedly ordering troops to kill protesters during last year's 18-day uprising, as well as corruption charges.
Moderate Islamist presidential candidate Abdel-Moneim Abul-Fotouh also spoke out against Suleiman's candidacy via Twitter Friday.
"Our battle is that of revolution or no revolution. If those who negotiated on behalf of the revolutionaries' murderers pitch their bid for presidency, it insults those who have sacrificed their lives to put an end to the police state. Those who were able to bring down the head of a regime will know to how to remove its tails," Abul-Fotouh posted on Twitter.
Suleiman must collect 30,000 recommendation forms from citizens to officially run in Egypt's first presidential elections.
Meanwhile, the Egyptian Foreign Ministry's request for an extension in the period of registration for absentee voters has been accepted, BikyaMasr.com reported.
Absentee voters now have until April Wednesday to register to vote in the presidential election, scheduled for May 23-24, Foreign Ministry spokesman Amr Roshdy said.